Factoring Quadratic Equations

There are several techniques that can be used to factor quadratic equations.
In this lesson, we will learn how to factor quadratic equations, where the coefficient of x2 is greater than 1, using the trial and error method. In this method, we will need to try out different possibilities to get the
right factors for the given quadratic equation. In this lesson, we will also learn how to factor quadratic equations by grouping

If the Coefficient of x2 Is Greater Than 1

Sometimes the coefficient of x in quadratic equations may not be 1, but the expression can be simplified by first finding common factors.

When the coefficient of x2 is greater than 1 and we cannot simplify the quadratic equation by finding common factors, we would need to consider the factors of the coefficient of x2 and the factors of c in order to get the numbers whose sum is b. If there are many factors to consider you may want to use the quadratic formula instead.

Example 1: Get the values of x for the equation 2x2 – 14x + 20 = 0

Step 1: Find common factors if you can.

2x2 – 14x + 20 = 2(x2 – 7x + 10)

Step 2: Find the factors of (x2 – 7x + 10)

List out the factors of 10:
We need to get the negative factors of 10 to get a negative sum. –1 × –10, –2 × –5

Step 3: Write down the different combinations of the factors and perform the distributive property to check. When there are many factors to check, this becomes a tedious method to solve such quadratic equations, so you may want to try the quadratic formula instead.

How to solve quadratic equations by factoring?
The method for solving quadratic equations by factoring is based on the zero-factor property of real numbers.
The zero factor property states that it two numbers a and b are multiplied together and the rsulting product is 0, then at least one of the numbers must be 0.

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